Simplify the following expression: $\dfrac{16x^5}{14x^4}$ You can assume $x \neq 0$.
Solution: $ \dfrac{16x^5}{14x^4} = \dfrac{16}{14} \cdot \dfrac{x^5}{x^4} $ To simplify $\frac{16}{14}$ , find the greatest common factor (GCD) of $16$ and $14$ $16 = 2 \cdot 2 \cdot 2 \cdot 2$ $14 = 2 \cdot 7$ $ \mbox{GCD}(16, 14) = 2 $ $ \dfrac{16}{14} \cdot \dfrac{x^5}{x^4} = \dfrac{2 \cdot 8}{2 \cdot 7} \cdot \dfrac{x^5}{x^4} $ $\phantom{ \dfrac{16}{14} \cdot \dfrac{5}{4}} = \dfrac{8}{7} \cdot \dfrac{x^5}{x^4} $ $ \dfrac{x^5}{x^4} = \dfrac{x \cdot x \cdot x \cdot x \cdot x}{x \cdot x \cdot x \cdot x} = x $ $ \dfrac{8}{7} \cdot x = \dfrac{8x}{7} $